Profit, Loss & Discount

Profit, Loss & Discount

Concept

Profit and loss are fundamentally percentage calculations on the cost price. The selling price (SP) is what the buyer pays, cost price (CP) is what the seller spends. When SP > CP, profit = SP − CP; when SP < CP, loss = CP − SP. The complication in SSC questions is that overhead costs (transport, packaging, octroi) must be added to CP before calculating profit/loss, and discounts are always applied on the marked price (MP), not the cost price.

Discount questions involve three prices: MP (what the seller initially tags), SP (what the buyer actually pays), and CP (what the seller paid). A common Tier 2 question is: “A shopkeeper gives a discount of 20% and still makes a 10% profit. Find the markup percentage” — meaning by how much above cost did he mark the price initially?

Fake transactions and weighing errors are a recurring theme: if a shopkeeper uses false weights (sells 900g when claiming 1kg), his effective profit is calculated on the difference.

Key Points

• Gain% = (Gain/CP) × 100. Loss% = (Loss/CP) × 100. Always take CP as base for percentages.
• When a transaction involves profit of x% and loss of y% on false weights, effective profit = x + y + xy/100.
• Discount is always on MP. Profit/Loss is always on CP.
• If SP with two different profit percentages is equal, CP can be found using the weighted average formula.
• Markup = (MP − CP)/CP × 100. After discount d%, SP = MP × (1 − d/100).

Worked Example

Q: A shopkeeper buys an article at 20% below its marked price. He sells it at a 10% discount on the marked price. Find his profit percent. Approach: Let MP = ₹100. CP = 100 − 20% of 100 = ₹80. SP = 100 − 10% of 100 = ₹90. Profit = 90 − 80 = ₹10 on CP ₹80. Profit% = 10/80 × 100 = 12.5%. Answer: 12.5%

SSC Pattern / Tips

• When the same article is sold at different profit/loss percentages to different customers at the same cost, compare total profits.
• For dishonest dealings (false weights), convert to price per kg equivalents to find effective gain%.
• In successive discount problems, first find the final SP from MP, then compare to CP for profit/loss.
• Watch for questions where discount% and profit% are the same number — this is a common pattern.